= P(R) - D[Qf(R|R)||P(R|R)].

We can see that Eq.(REF ) is exactly the objective function of a VAE [1]}.
Specifically, the real user preference \(\textbf {R}\)  is the latent variables. \(Q_f(\textbf {R}|\tilde{\textbf {R}})\)  which is parameterized by our target model \(f_\theta \) 
maps the corrupted data \(\tilde{\textbf {R}}\)  to the latent variables \(\textbf {R}\)  and thus can be seen as the encoder. The likelihood \(P(\tilde{\textbf {R}}|\textbf {R})\)  describes the distribution of corrupted data \(\tilde{\textbf {R}}\)  given the real user preference \(\textbf {R}\)  and acts as the decoder. Finally, \(P(\mathbf {R})\)  is the fixed prior distribution. This leads to our second proposed learning framework DVAE.
